init

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l4/.gitignore

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+*.zip

l4/z1/.gitignore

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l4/z1/rsa-rs/.gitignore

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+/target

l4/z1/rsa-rs/Cargo.lock

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+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 3
+
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l4/z1/rsa-rs/Cargo.toml

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+[package]
+name = "rsa"
+version = "0.1.0"
+edition = "2021"
+
+[dependencies]
+rand = "0.8.5"
+num-bigint = { version = "0.4.5", features = [ "rand" ] }
+num-traits = "0.2.19"

l4/z1/rsa-rs/src/main.rs

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+use rand::thread_rng;
+use num_bigint::{BigInt, BigUint, RandBigInt, ToBigInt};
+use num_traits::{One, Zero};
+
+#[derive(Clone, Debug, PartialEq)]
+struct Key {
+    n: BigUint,
+    key: BigUint,
+}
+
+#[derive(Clone, Debug, PartialEq)]
+struct KeyPair {
+    private: Key,
+    public: Key,
+}
+
+fn is_prime(n: &BigUint) -> bool {
+    let mut i = BigUint::from(2u32);
+    while &i < &n.sqrt() {
+        if n % &i == 0u32.into() {
+            return false;
+        }
+        i += 1u32;
+    }
+    true
+}
+
+fn euclid(a: &BigUint, b: &BigUint) -> BigUint {
+    let mut s0 = BigInt::one();
+    let mut s1 = BigInt::zero();
+    let mut t0 = BigInt::zero();
+    let mut t1 = BigInt::one();
+    // SAFETY: according to the docs this will never fail
+    // https://docs.rs/num-bigint/latest/num_bigint/trait.ToBigInt.html
+    let mut r0 = a.to_bigint().unwrap();
+    let mut r1 = b.to_bigint().unwrap();
+
+    while r1 != 0.into() {
+        let q = &r0 / &r1;
+        let mut temp = r1.clone();
+        r1 = r0 - &q * r1;
+        r0 = temp;
+
+        temp = s1.clone();
+        s1 = s0 - &q * s1;
+        s0 = temp;
+
+        temp = t1.clone();
+        t1 = t0 - &q * t1;
+        t0 = temp;
+    }
+
+    // SAFETY: this if prevents the result from being negative
+    if s0 < 0.into() {
+        (s0 + BigInt::from(b.clone())).to_biguint().unwrap()
+    } else {
+        s0.to_biguint().unwrap()
+    }
+}
+
+fn find_e(phi: &BigUint) -> BigUint {
+    let mut e = thread_rng().gen_biguint_range(&1u32.into(), phi);
+    let mut g = gcd(&e, phi);
+    while g != 1u32.into() {
+        e = thread_rng().gen_biguint_range(&1u32.into(), phi);
+        g = gcd(&e, phi);
+    }
+
+    e
+}
+
+fn generate_key_pair(p: &BigUint, q: &BigUint) -> Option<KeyPair> {
+    if !is_prime(p) || !is_prime(q) || p == q {
+        return None;
+    }
+
+    let n = p * q;
+    let phi = (p - 1u32) * (q - 1u32);
+
+    let e = find_e(&phi);
+
+    let d = euclid(&e, &phi);
+
+    Some(
+        KeyPair {
+            private: Key { n: n.clone(), key: d },
+            public: Key { n, key: e }
+        }
+    )
+}
+
+fn gcd(a: &BigUint, b: &BigUint) -> BigUint {
+    if b > a {
+        return gcd(b, a);
+    }
+    let mut a = a.clone();
+    let mut b = b.clone();
+    let mut r;
+    while b != BigUint::zero() {
+        r = a % &b;
+        a = b;
+        b = r;
+    }
+    a
+}
+
+fn pow_mod(a: &BigUint, exp: &BigUint, n: &BigUint) -> BigUint {
+    let mut a = a.clone();
+    let mut exp = exp.clone();
+    let mut res = BigUint::one();
+    while exp > BigUint::zero() {
+        if &exp % 2u32 == 1u32.into() {
+            res = (res * &a) % n;
+        }
+        a = (&a * &a) % n;
+        exp /= 2u32;
+    }
+    res
+}
+
+fn find_private_key(n: &BigUint, e: &BigUint, d: &BigUint) -> (BigUint, BigUint) {
+    let kphi = d * e - 1u32;
+    let mut t = kphi.clone();
+    while &t % 2u32 == BigUint::zero() {
+        // println!("t: {t}");
+        t /= 2u32;
+    }
+    
+    let mut p = BigUint::one();
+
+    let mut a = BigUint::from(2u32);
+    while a < 100u32.into() {
+        let mut k = t.clone();
+        while k < kphi {
+            // println!("a: {a}, kphi: {kphi}, k: {k}, n: {n}");
+            let x = pow_mod(&a, &k, n);
+            // println!("x: {x}; n: {n}");
+            if x != BigUint::one() &&
+                x != (n - 1u32) &&
+                pow_mod(&x, &2u32.into(), n) == BigUint::one()
+            {
+                // println!("x: {x}; n: {n}");
+                p = gcd(&(x - BigUint::one()), n);
+                // println!("p: {p}");
+                break;
+            }
+            k *= 2u32;
+        }
+        a += 2u32;
+    }
+
+    let q = n / &p;
+
+    (p, q)
+}
+
+fn main() {
+    let p1 = BigUint::from(1234577u32);
+    let p2 = BigUint::from(1234567891u32);
+
+    let pair_a = generate_key_pair(&p1, &p2)
+        .expect("failed to generate key pair a");
+
+    let pair_b = generate_key_pair(&p1, &p2)
+        .expect("failed to generate key pair b");
+
+    println!("private key A: {:?}", pair_a.private);
+    println!("public key A: {:?}", pair_a.public);
+    println!("private key B: {:?}", pair_b.private);
+    println!("public key B: {:?}", pair_b.public);
+
+    let found_secret = find_private_key(&pair_a.public.n, &pair_a.public.key, &pair_a.private.key);
+    println!("found_b: {:?}", found_secret);
+    if (&found_secret.0 == &p1 && &found_secret.1 == &p2)
+        || (&found_secret.0 == &p2 && &found_secret.1 == &p1) {
+        println!("cracked B)");
+    } else {
+        println!("uncracked B(");
+    }
+}